Solve each inequality and describe the steps
|1.3x + 7.8| > 0

The required value of y is 5/8.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant  of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

let k be the constant of proportion

When a quantity varies directly with others, then we have a relation, y = kx      —-- 1

Now, find k for given x = 4 and y = ½, we need to put these values in equation 1, i.e.

½ = k(4)

k = ⅛

Further calculate y for given x = 5 and constant of proportion, k = 1/8 i.e.

y = (⅛)(5)

y = 5/8

Hence, the required value of y is 5/8.

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The number of hours that the kayak rented for the total costs to be the same will be 2 hours.

At 1 hour, the cost will be:

y = 7x + 9

= 7(1) + 9 = 16

At 2 hours, cost will be:

y = 7x + 9

y = 7(2) + 9

= 23

It should be noted that in the table, at 2 hours the cost is $23 also. Therefore, the number of hours that the kayak rented for the total costs to be the same will be 2 hours.

Also, shop B charges less per hour.

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Hi ~

* ˚ ✦ E x p l a n a t i o n : - * ˚ ✦

Combine multiplied terms into a single fraction.

[tex]\bold{(\frac{1}{2} \: a \: + \: 2d)^2}[/tex]

[tex]\bold{(\frac{1a}{2} \: + \: 2d)^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Multiply by 1.

[tex]\bold{(\frac{1a}{2} \: + \: 2d)^2}[/tex]

[tex]\bold{(\frac{a}{2} \: + \: 2d)^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Find common denominator.

[tex]\bold{(\frac{a}{2} \: + \: 2d)^2}[/tex]

[tex]\bold{(\frac{a}{2} \: + \: \frac{2 \: ^. \: 2d}{y})^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Combine fractions with common denominator.

[tex]\bold{(\frac{a}{2} \: + \: \frac{2 \: ^. \: 2d}{y})^2}[/tex]

[tex]\bold{(\frac{a \: + \: 4}{2})^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Multiply the numbers.

[tex]\bold{(\frac{a \: + \: 2 \: ^. \: 2d}{2})^2}[/tex]

[tex]\bold{\frac{(a \: + \: 4d \: ^. \: 2d)}{2^2}^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Distribute exponent.

[tex]\bold{(\frac{a \: + \: 4d}{2}^2)}}[/tex]

[tex]\bold{\frac{(a \: + \: 4d)}{2}^2}[/tex]

﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌

Evaluate the exponent.

[tex]\bold{\frac{(a \: + \: 4d)}{2^2}^2}}[/tex]

[tex]\bold{\frac{(a \: + \: 4d)}{4}^2}}[/tex]

Your answer would be is:

[tex]{\huge{\boxed{\bold{{\rightarrow{\frac{(a \: + \: 4d)}{4}^2}}}}[/tex]

Hope It Helps...

[tex]\textsc{Answer:}[/tex]

TheAestheticGirl

Answer:

B

Step-by-step explanation:

Let's start by evaluating each of the equations:

[tex]y\geq 2x+7[/tex]

To begin to understand this equation, first, graph line by replacing the inequality symbol with an equal sign:

The graph of this line is the first attached image at the bottom of this answer.

The inequality reads, y is greater than or equal to 2x + 7.

The "equal to" is very important. This means that the line [tex]y= 2x+7[/tex] is a solution to this problem, so the line is drawn as a SOLID line.

Because the inequality is GREATER than, that means that all values greater than the function are solutions! Thus the area  ABOVE the line is shaded. The second image attached below shows the shaded graph.

Now, let's look at the second equation:

[tex]y > -\frac{1}{3} x-2[/tex]

Start by replacing the inequality symbol with an equal sign and graphing the line. See the third image below for that line.

Now, THIS inequality is just GREATER than, not equal to. This means that the line that we just graphed, [tex]y = -\frac{1}{3} x-2[/tex] is NOT a solution to the equation! Therefore, the line is drawn as a dashed line. This means it is NOT included in the solution.

Again, since it is greater than, the area ABOVE the line is shaded. See the fourth image attached below to see the graph.

Now, let's combine these graphs! In the fifth image below, the blue represents [tex]y\geq 2x+7[/tex], and the red represents [tex]y > -\frac{1}{3} x-2[/tex].

The area where the red and blue overlap is the area to keep for the solution of this problem, since these equations represent a system of linear inequalities. I hope this helped!

Answer: y= 2/5x+12/5

Step-by-step explanation:

when you subtract 2x from both sides you get

-5y=-12-2x

and then you divide by -5 to get

y=-12-2x/-5

and you see that all the terms have negatives so you can just change them all to positives to get

y=12+2x/5

and then making the equation into y=mx+b format (which is prettier)

you get y=2/5x+12/5

yw

Step-by-step explanation:

2x - 5y= - 12

-2× -2x

0 -5y = -12 - 2x

÷-5y ÷-5y ÷-5y

y = 12/5 + 2x/5 or y = 2x/5 + 12/5

(its recommended to but the variable number in front)

Answer:

6 3/14

Step-by-step explanation:

[tex]4\:1/7 \div 2/3 = 29/7 \div 2/3\\= 29/7 \div 2/3\\= \frac{29*3}{7*2}\\= 87/14\\= 6\:3/14[/tex]

The average temperature decrease of -6.5 degrees/km Celsius is known as Normal lapse rate.

Normal lapse rate is defined as the decrease in the temperature while moving upwards in the atmosphere. Normally, the rate of decrease is 1 degree Celsius for every 165 meter rise in altitude or we can say that it is 6.5 degree Celsius for every 1 km rise in altitude.

This lapse rate is known as normal lapse rate or environmental lapse rate.

This is why when we move higher in the atmosphere, we experience low temperatures. On average this decrease is equal to the amount of temperature as discussed in the normal lapse rate.

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According to the given data young's modulus for this material = 5.73 *(10^8 ) pa

Young's modulus (E) of material seems to be the ratio of compressive loading () to tensile strain (). Where stress is defined as the amount of normal force per unit area ( = F/A) and strain is defined as extension per unit length ( = dl/l).

Youngs modulus Y of a material is given Y = FL/ADL

where

A = area

DL = change of length

L = original length

F = force

so here we apply

Y = 65*9.8* 45/(3.14* 3.5*3.5* 10^-6 * 1.3)

Y = 5.73 *(10^8 ) pa

According to the given data young's modulus for this material = 5.73 *(10^8 ) pa

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I understand that the question you are looking for is:

A nylon rope used by mountaineers elongates 1.30 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young's modulus for this material?

A group of products are averaged to determine central tendency using the geometric mean. The geometric mean of 7 and 12 is 2√21.

The geometric mean in mathematics is a mean or average that, by using the product of the values of the numbers, shows the center tendency or usual value of a set of numbers.

The geometric mean, sometimes known as the compounded annual growth rate, is a tool used in finance to determine average growth rates.

The Geometric Mean (GM) is the average value or mean that reveals the central tendency of a group of numbers by adding up the values of those numbers.

Formula to calculate Geometric Mean is

x = √(a × b)

Where, a = 7 and b = 12

x = √(7 × 12)

x = √(7 × 4 × 3)

x = 2√21

The value of x = 2√21.

Therefore, the geometric mean between the pair of numbers 7 and 12 is 2√21.

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Answer:

Step-by-step explanation:

Answer:

y=17.50n+80.00 202.50

Step-by-step explanation:

y=17.50n+80.00

N is hours

Make N=7

17.50*7=122.50

80+122.50=202.50

To make a line perpendicular, flip the denominator and numerator of the slope and make it positive if it was negative or negative if it was positive.

In this case, our slope is 3, so to make a perpendicular line, it would become: [tex]-\frac{1}{3}[/tex]

Now to make it pass through -6, 3 we need to plug in those numbers, and we'll be removing the 3 added at the end.

x = -6

y = 3

y = x

3 = [tex]-\frac{1}{3}[/tex](-6)

3 = 2

In order to make this true, we need to add 1 to the right side.

3 = 2 + 1

3 = 3

So, the equation would be  [tex]y=-\frac{1}{3}x+1[/tex]

By substitution, the solution of the system of equations, 3x - y = 5 and y = 4x + 2, is (-7 , -26).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Given two linear equations in x and y,

3x - y = 5     (equation 1)

y = 4x + 2     (equation 2)

Use substitution method since the second equation is already expressed in y in terms of x. Substitute the value of y to the first equation.

3x - y = 5     (equation 1)

3x - (4x + 2) = 5

3x - 4x - 2 = 5

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.

3x - 4x - 2 = 5

3x - 4x = 5 + 2

-x = 7

x = -7

Substitute the value of x in the second equation and solve for y.

y = 4x + 2     (equation 2)

y = 4(-7) + 2

y = -28 + 2

y = -26

Hence, the solution of the given system of equations is (-7 , -26).

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Answer:

5

Hope this helps :)

Step-by-step explanation:

1. Solve by adding since a = 2 and b = 3.

2 + 3 = 5

Check:

5 - 3 = 2 ✓

With each line, a slope-intercept relationship (4,-1) and (-2,-1).

Y = 0 ,X = 5.

The slope-intercept form is just a means of stating a line's equation so that both the slope (steepness) as well as y-intercept (where another line crosses this same vertical y-axis) are obvious. This expression is frequently referred to as y = mx + b.

To begin, are using the slope formula to figure out the average slope between two points here.

Let:

x1 = 4

y1 = -1

x2 = -2

y2 = -1

m = (y2-y1)/(x2-x1)

= (-1 - (-1))/ (4-(-1))

= 0/5

= 0

So the slope is 0.

We must now calculate the y-intercept. This will be accomplished by converting a single of the points and also the slope together into a point-slope linear equation. y2-y1 = m(x2-x1).

Let’s plug in the point (5,0).

So we get y-(-0) = (0/5)(x-(-5)) ⇒  y+0

= (0/5)x +  0 ⇒  y

So,

Y = 0

X = 5

with each line, a slope-intercept relationship (4,-1) and (-2,-1).

Y = 0 ,X = 5

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Answer:

Step-by-step explanation:

Answer:

18x+66=6(3x+11) square feet

Step-by-step explanation:

Answer:

7.8

-1/5

-16.2

5 5/8

Step-by-step explanation:

Answer:

8.7

Hope this helps <3

Have a great day!

Answer:

C=r-p

Step-by-step explanation:

r-c=p

We need to solve the equation for Variable C

To get c alone we need to remove r from the left hand side

Subtract R from both sides

r-c=p

r-r-c=-r+P

-c=-r+P

Now divide both sides by -1 to get c alone

c=r-p

C is alone, it is solved for C

The volume of the larger suitcase, a rectangular prism 85 centimeters long, is 168,539.1 cubic cm.

Solids of the same type that have proportional corresponding linear

measures are similar solids. In the case of similar rectangular prisms:

length of A / length  of B = width of A / width of B = height of A / height of B

Using this scale, if the larger suitcase is 85 centimeters long, and the smaller suitcase is 68 centimeters long, 47 centimeters wide, and 27 centimeters deep, then:

length of larger suitcase / length of smaller suitcase = 85 cm / 68 cm = 5/4

width of larger suitcase / width of smaller suitcase = 5/4

width of larger suitcase = 5/4 (47 cm)

width of larger suitcase = 58.75 cm

depth of larger suitcase / depth of smaller suitcase = 5/4

depth of larger suitcase = 5/4 (27 cm)

depth of larger suitcase = 33.75 cm

Solving for the volume of the larger suitcase using the formula for the volume of rectangular prism:

V = lwh

V = 85 cm (58.75 cm) (33.75 cm)

V = 168,539.0625 cubic cm

Rounding off to the nearest tenth.

V = 168,539.1 cubic cm

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Answer:

4.775278.

Step-by-step explanation:

4.77527806851, when rounded to nearest millionth results in 4.775278.

Answer: 4.775278

Step-by-step explanation:

The place values go tenth, hundredth, thousandth, ten thousandth, hundred thousandth, and millionth. The place value after that is zero, so it stays as eight.

The square root of (1/96) is the same as the square root of 1 divided by the square root of 96. You can divide the fraction inside the radical before or after you calculate the square root. The result will be the same.

Here we first calculate the square root of the numerator and the square root of the denominator separately, and then we divide the two:

[tex]\frac{\sqrt{1}}{\sqrt{96} }[/tex] ≈ [tex]\frac{1}{9.798}[/tex]  ≈  0.1021

Alternatively, we first divide 1 by 96 and then do the square root of the quotient:

[tex]\sqrt{1/96}[/tex] ≈ [tex]\sqrt{0.0104}[/tex] ≈ 0.1021

To calculate the square root of 1 divided by 96, you first take the square root of 1 and then divide that result by 96:

[tex]\frac{\sqrt{1}}{96} = \frac{1}{96}[/tex] ≈  0.0104

The correct statements for the function are given as follows:

A. The domain for the function is all real values.

B. The range for the function is the set {-5}.

For this problem, the function assumes the value y = -5 for all real values of x, hence statements A and B are correct, while D is not.

The graph also represents a function, as each value of x is associated with only one value of y.

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Answer:

Solution on screen

Step-by-step explanation:

I hope it's clear

The solution of the equation 2/y + 1/2 = 5/2y is y = 1

In this question, we have been given an equation.

2/y + 1/2 = 5/2y

We need to find the solution of given equation.

⇒ 2/y + 1/2 = 5/2y

⇒ (4 + y)/2y = 5/2y

⇒ 4 + y = 5

⇒ y = 5 - 4

⇒ y = 1

We need to check above solution.

So, substitute y = 1 in given equation.

⇒ 2/y + 1/2 = 5/2y

⇒ 2/(1) + 1/2 = 5/2(1)

⇒ 2 + 1/2 = 5/2

⇒ 5/2 = 5/2

⇒ LHS = RHS

Therefore, the solution of the equation 2/y + 1/2 = 5/2y is y = 1

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Answer:

Manisha is 36 and Rahul is 6.

Step-by-step explanation:

Let m = Manisha's current age

Let r - Rahul's current age.

Today:

m = 6r

In for years:

m+ 4 = 4(r + 4) Distribute the 4

m + 4 = 4r + 16  Substitute in 6r for me

6r + 4 = 4r + 16  Subtraction 4r from both sides

2r + 4 = 16  Subtract 4 from both sides

2r = 12  Divide both sides by 2

r = 6  Rahul is 6  Plug 6 for r into either of the two original equations to find Manisha's age.

m = 6r

m = 6(6)

m = 36

Rahul's present age is 6 years, and Manisha's present age is 36 years.

Let's use the letters "M" for Manisha's current age and "R" for Rahul's.

Given information:

1. Manisha's age is 6 times Rahul's age: M = 6R

2. After 4 years, Manisha's age will be four times Rahul's age: M + 4 = 4(R + 4)

We have a system of two equations with two variables. We can use these equations to solve for their present ages.

Equation 1: M = 6R

Equation 2: M + 4 = 4(R + 4)

Substitute the value of M from Equation 1 into Equation 2:

6R + 4 = 4(R + 4)

Distribute the 4 on the right side:

6R + 4 = 4R + 16

Subtract 4R from both sides:

2R + 4 = 16

Subtract 4 from both sides:

2R = 12

Divide by 2:

R = 6

Now that we know Rahul's age (R = 6), we can find Manisha's age using Equation 1:

M = 6R = 6 × 6 = 36

So, Manisha is 36 years old and Rahul is 6 years old at the moment.

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